Polynomial Representation

Abstract

For linear systems, the state-space representation and the polynomial representation are conceptually equivalent, but the classical state-space representation does not make it possible to access the partial transfer functions between inputs (control variables or disturbances) and different components of the output. This is the reason why we use representations that make it easy to compute the different transfer functions connecting inputs and outputs, called polynomial representations. Then, it is interesting to use the degrees of freedom in the control to place zeros in suitable transfer functions between some disturbances and some outputs. This makes it possible to reject these disturbances with a minimal size controller.